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3 years ago

Which expression is equivalent to (xy^-6)^2

Mathematics

1 answer:

Furkat [3]3 years ago

4 0

Answer:

$\huge\boxed{\left(xy^{-6}\right)^2=x^2y^{-12}=\dfrac{x^2}{y^{12}}}$

Step-by-step explanation:

$\left(xy^{-6}\right)^2=x^2\left(y^{-6}\right)^2=x^2y^{-6\cdot2}=x^2y^{-12}=\dfrac{x^2}{y^{12}}$

Used

$(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\dfrac{1}{a^n}$

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Can anyone explain how this is done.

Softa [21]

Answer:

The answer is C. How many 3/4 -pound molds are in 1/3 pound of sand?

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3 years ago

Read 2 more answers

Two basketballs are thrown along different paths. Determine if the basketballs’ paths are parallel to each

Paul [167]

Answer:

Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.

Step-by-step explanation:

Remember that:

Two lines are parallel if their slopes are equivalent.
Two lines are perpendicular if their slopes are negative reciprocals of each other.
And two lines are neither if neither of the two cases above apply.

So, let's find the slope of each equation.

The first basketball is modeled by:

$\displaystyle 3x+4y=12$

We can convert this into slope-intercept form. Subtract 3<em>x</em> from both sides:

$4y=-3x+12$

And divide both sides by four:

$\displaystyle y=-\frac{3}{4}x+3$

So, the slope of the first basketball is -3/4.

The second basketball is modeled by:

$-6x-8y=24$

Again, let's convert this into slope-intercept form. Add 6<em>x</em> to both sides:

$-8y=6x+24$

And divide both sides by negative eight:

$\displaystyle y=-\frac{3}{4}x-3$

So, the slope of the second basketball is also -3/4.

Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.

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3 years ago

Which step is wrong, Step 1, Step 2, Step 3 or Li didn't make a mistake

mart [117]

Hello there!

The correct answer is option A

Instead of the division sign, it suppose to be multiply.

Have fun on Khan Academy!

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3 years ago

Businesses deposit large sums of money into bank accountsImagine an account with $10 million dollars in it.

adoni [48]

again, let's assume daily compounding means 365 days per year.

$~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (10000000)(0.0212)(1)\implies \boxed{I=212000}$

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &1 \end{cases}$

$A=10000000\left(1+\frac{0.0212}{365}\right)^{365\cdot 1}\implies A\approx 10214256.88 \\\\\\ \underset{\textit{earned interest amount}}{10214256.88~~ - ~~10000000 ~~ \approx ~~ \boxed{214256.88}}$

what's their difference? well

$\stackrel{\textit{compounded daily}}{\approx 214256.88}~~ - ~~\stackrel{\textit{simple interest}}{212000}\implies \boxed{2256.88}$

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2 years ago

A pair of boots is on sale for 1/4 off the original price. The sale price is $70.50. What is the original price of the boots?

Iteru [2.4K]

Answer: 282

Step-by-step explanation: just multiplícate it by 4

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3 years ago